A newly found x-ray diffraction band, obtained from aqueous solutions of soaps and detergents, gives a Bragg spacing which is independent of concentration and is close to the double-length of the molecule. This is designated as the micelle thickness or M-band. The already known long-spacing band, interpreted here as related to the inter-micellar distance, is designated as the I-band. Its spacing dI increases with decreasing soap concentration. If a hydrocarbon is solubilized in the micelles, these spacings increase by ΔdM and ΔdI. Formerly, ΔdI was supposed to give the mean thickness of the layer of oil dissolved between the ends of the hydrocarbon chains of the soap molecules as a middle layer in the micelle. However, ΔdM seems to be more directly related to this thickness. As measured by dM, the thickness of the micelle remains constant with increasing soap concentration: e.g., the values are 40.8, 41.5, 40.7, 40.2, 39.5, 39.6, 40.2A for potassium myristate at 25°C at the following respective concentrations: 2.3, 4.5, 7.2, 9.8, 12.0, 13.7, and 16.5 percent. The mean ``thickness'' increases from 29.7A for potassium caprylate (C8) to 47.3 for potassium palmitate (C16). By a method explained in the text, the number of molecules in a potassium myristate micelle is calculated as 56 at 9.8 percent by use of the Bragg I-spacing. However, it is probable that a corrected Bragg spacing should be used. A new long-spacing band, designated as an X-band, appears when an I-band is present and oil is solubilized in the micelles. The order of spacing is then dI>dM>dX; e.g., in one case the values are 84>50>27A. The ``cylindrical'' model of the micelle preferred here differs from the lamellar and in some respects from the spherical model. It exhibits the following characteristics: (1) A micelle consists of one double-layer of soap or detergent molecules. These have their polar ends oriented outward toward the water and their non-polar ends inward toward each other. (2) The thickness of the micelle of a pure soap is essentially twice the length of the soap molecule, independent of concentration. (3) Hydrocarbons solubilize inside the micelle between the two layers of soap molecules and thus make he micelle thicker. (4) The area per soap molecule in the micelle remains practically constant, whether or not solubilized hydrocarbons are present. (5) The width or lateral dimension of the micelle and the number of soap molecules per micelle increase with increasing soap concentration and with solubilization of hydrocarbons. (6) From energy considerations the area of contact between the hydrocarbon chains of the detergent molecules and the water must be as small as is compatible with the other conditions imposed upon its structure.
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